Introduction to KAM theory

Abstract

This thesis aims to provide an introduction to modern KAM theory. This objective is accomplished by introducing the fundamental ideas of KAM theory, including its background, commonly used methods, and the general structure of a KAM proof. Additionally, the thesis discusses parameter reduction and the generalizations of the Diophantine conditions. The culmination of the thesis is a complete proof of the classical KAM theorem, but the primary focus remains pedagogical and expository throughout. It is important to note that while the thesis covers a broad range of topics, it does not aim to provide a systematic survey of all the methods found in KAM theory. Instead, the emphasis is on presenting the traditional KAM method and its key ideas in a clear and accessible manner.